A study of the optimal measurement placement for parameter identification of orthotropic composites by the boundary element method

This paper concentrates on the design of the optimal measurement placement for the parameter identification of two-dimensional orthotropic composites, which is modeled by the boundary element. From the analysis of the well-posedness of the parameter identification processes using the Levenberg–Marquardt method, a performance indicator and an estimation of the maximum bias of identified parameters are deduced. Based on these results, a method for selecting the optimal measurement placement is proposed. The validity of this method is illustrated by some numerical examples. These examples reveal that the measurement placement has significant influence on identification results. Furthermore, an iterative process of selecting measurement placement is suggested for practical implementation.     

The effect of boundary conditions on the dynamic stability of orthotropic cylinders using a modified exact analysis

A calculation of overall dynamic response of thin orthotropic cylindrical shells is presented. Due to the obvious importance of the effects of transverse shear deformation and rotary inertia, these terms are included in the analysis. The exact method is modified to predict the dynamic behavior of an orthotropic circular cylindrical shell. The modal forms are assumed to have the axial dependence in the form of a simple Fourier series. By using the present modified exact analysis various aspects such as influence of boundary conditions, changes in shell geometrical parameters, changes in the directions of orthotropy, etc., on the frequencies, mode shapes and modal forces are studied. Analytical results are shown to be in good agreement with some available experimental and theoretical results.     

Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach

A new computational method based on the equivalent domain integral (EDI) is developed for mode I fracture analysis of orthotropic functionally graded materials (FGMs) subjected to thermal stresses. By using the constitutive relations of plane orthotropic thermoelasticity, generalized definition of the J-integral is converted to an equivalent domain integral to calculate the thermal stress intensity factor. In the formulation of the EDI approach, all the required thermomechanical properties are assumed to have continuous spatial variations through the functionally graded medium. Developed methodology is integrated into a fracture mechanics research finite element code FRAC2D using graded finite elements that possess cubic interpolation. Steady-state and transient temperature distribution profiles in orthotropic FGMs are computed using the finite elements based heat transfer analysis software HEAT2D. EDI method is validated and domain independence is demonstrated by comparing the numerical results obtained using EDI to those calculated by an enriched finite element method and to those available in the literature. Single and periodic edge crack problems in orthotropic FGMs are examined in order to study the influences of principal thermal expansion coefficient and thermal conductivity components, relative crack length and crack periodicity on the thermal stress intensity factors. Numerical results show that among the three principal thermal expansion coefficient components, the in-plane component perpendicular to the crack axis has the most significant influence on the mode I stress intensity factor. Gradation profile of the thermal expansion coefficient parallel to the crack axis is shown to have no effect on the outcome of the fracture analysis.     

Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory

A two-dimensional global higher-order deformation theory is presented for thermal buckling of cross-ply laminated composite and sandwich plates. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through the principle of virtual work. Several sets of truncated Mth-order approximate theories are applied to solve the eigenvalue problems of a simply supported multilayered plate. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. Numerical results are compared with those of the published three-dimensional layerwise theory in which both in-plane and normal displacements are assumed to be C⁰ continuous in the continuity conditions at the interface between layers. Effects of the difference of displacement continuity conditions between the three-dimensional layerwise theory and the global higher-order theory are clarified in thermal buckling problems of multilayered composite plates.     

Novel beam analysis of end notched flexure specimen for mode-II fracture

A novel beam model of end notched flexure (ENF) specimen for mode-II fracture testing is presented. By applying the principle of superposition, the ENF specimen is modeled as two sub-problems: (1) an un-cracked beam under three-point bending; and (2) a skew symmetric cracked beam under shear traction on the crack surface. Due to skew-symmetry of sub-problem two, only the upper half of the beam is analysed, and based on compatibility of deformation, a shear compliance coefficient is introduced to establish beam deformation equation. Explicit and simple closed form solutions of compliance and strain energy release rate are obtained, and they compare well with existing finite element analyses. Compared to other available analytical methods of the ENF specimen, the present beam model is relatively simple and easy to use; further, it can be applied to other beam fracture specimen analysis (e.g., mixed mode fracture and bi-material interface specimen).     

On Saint-Venant’s problem for anisotropic, inhomogeneous, cylindrical Cosserat elastic shells

We investigate the static deformation of cylindrical elastic shells, using the theory of Cosserat surfaces. We consider anisotropic and inhomogeneous cylindrical shells with arbitrary (open or closed) cross-section. The constitutive coefficients are assumed to be independent of the axial coordinate. In the context of linearized theory, we determine a solution of the relaxed Saint-Venant’s problem. Finally, we apply the general results in the special cases of circular cylindrical shells and of Cosserat plates made from an orthotropic material.     

A discontinuum-based model to simulate compressive and tensile failure in sedimentary rock

The study presented in this paper discusses a discontinuum-based model for investigating strength and failure in sedimentary rocks.The model has been implemented by UDEC to incorporate an innovative orthotropic cohesive constitutive law for contact.To reach this purpose,a user-defned model has been established by creating dynamic link libraries(DLLs)and attaching them into the code.The model reproduces rock material by a dense collection of irregular-sized deformable particles interacting at their cohesive boundaries which are viewed as flexible contacts whose stress-displacement law is assumed to control the fracture and the fragmentation behaviours of the material.The model has been applied to a sandstone.The individual and interactional effects of the microstructural parameters on the material compressive and tensile failure responses have been examined.In addition,the paper presents a new methodical calibration procedure to ft the modelling microparameters.It is shown that the model can successfully reproduce the rock mechanical behaviour quantitatively and qualitatively.The study also shows how discontinuum-based modelling can be used to characterize the relation between the microstructural parameters and the macro-scale properties of a material.     

Determination of material properties of orthotropic plates with general boundary conditions using Inverse method and Fourier series

Determination of material properties of orthotropic plates with general elastic boundary supports using the Inverse method is presented in this paper. The material properties were identified through updating four parameters in the governing equation of a symmetrically laminated thin plate. The sum of the squared difference of the natural frequencies obtained from modal testing was minimized using the Forward method. The displacement function was expressed as a 2-D Fourier cosine series supplemented with several terms in the form of 1-D series. A classical solution was derived by letting the series exactly satisfy the governing differential equation and all the boundary conditions at every field and boundary point. In the Inverse method, the series expansions for all the relevant derivatives of the eigen frequencies were obtained through term-by-term differentiations of the displacements. Many simulations were done but one numerical example is presented to demonstrate the accuracy and convergence of the solutions.     

Nonlinear vibration and stability of a shallow unsymmetrical orthotropic sandwich shell of double curvature with orthotropic core

In this paper, nonlinear behaviours for a shallow unsymmetrical, orthotropic sandwich shell of double curvature with orthotropic core having different elastic characteristics have been studied by a new set of uncoupled differential equations. The face sheet may be of unequal thickness of different materials. However, a restriction that the elements radii of curvature be large compared to the overall thickness of the sandwich has been imposed.

A simple approach used in the present analysis can be applied for stability as well as vibration. For the symmetrical case, where the face sheets are of equal thickness and of same materials, these equations can be shown to reduce to those given by Grigolyuk in 1957. Numerical results of a square rectangular simply supported curved plate, and of a rectangular sandwich cylindrical shell under mechanical and dynamic loading, have been computed and compared with other known results.     

Elastic–plastic stress analysis of an orthotropic rotating disc

In this study, the elastic–plastic stress analysis of a curvilinearly orthotropic rotating annular disc is investigated analytically for strain-hardening material behavior. To be able to see the separation of the plastic region, a few angular velocities are taken into consideration for such an analysis. Radial and circumferential stress components are obtained to increase angular velocity. It is seen that the magnitudes of the circumferential stress components are higher than those of the radial stress components. The magnitudes of the residual stress component of the circumferential stress and plastic flow are the highest at the inner surface. The radial displacements in both the elastic and plastic solutions calculated analytically have higher values at the inner surface than those of the outer surface for all the angular velocities.